Sensitivity Analysis of Domain Considerations for Numerical Simulations of Film Cooling

The majority of computational fluid dynamics studies for turbine film cooling have employed the Reynolds-Averaged Navier-Stokes equations with various turbulence modeling techniques to achieve closure, most notably the various two equation (k-ε or k-ω) models. For computational simulation of film cooling, modeling the entire testing domain with a row of multiple holes while sustaining a sufficiently fine mesh would demand a large number of grid cells and a hefty computational expense. A significant reduction in the computational domain can be and has been achieved without much harm to the overall accuracy of the film cooling prediction. The current study aimed to investigate the necessary domain parameters for reducing the grid cell count without significantly affecting the accuracy of the solution. The Box-Behnken design for response surface methodology was employed to determine the relative influence of each parameter on the cooling effectiveness prediction. The experimental design matrix was executed for multiple blowing ratios (0.5, 1.0, 2.0) to include the effects of the blowing ratio on the computational domain. The work was carried out using a three-dimensional computational fluid dynamics finite volume method with the RANS equations and k-ε turbulence model. A cylindrical film cooling hole with a pitch-to-diameter ratio of 3.0, a length-to-diameter ratio of 7.5, and an inclination angle of 35° was studied. The results are compared against existing data in the literature as well as in-house experimental data. The data from each case is compared in terms of spatially-averaged effectiveness. The modeled entrance length was found to be the most important parameter, with the mainflow height a distant second. The size of the modeled plenum was not found to exert any significant influence on the effectiveness results. Explanations are offered for notable trends in the data and conclusions are drawn concerning the grid optimization process.